A Fej\'{e}r theorem for boundary quotients arising from algebraic dynamical systems

TL;DR

This paper proves a Fejér-type theorem for boundary quotients of $C^*$-algebras linked to algebraic dynamical systems, enhancing understanding of their structural properties.

Contribution

It introduces a Fejér theorem in the context of boundary quotients from algebraic dynamical systems, advancing the analysis of their algebraic structure.

Findings

Established a Fejér-type approximation theorem for boundary quotients.

Strengthened the understanding of the relative commutant structure.

Provided new tools for analyzing $C^*$-algebras from dynamical systems.

Abstract

A Fej\'{e}r-type theorem is proved within the framework of $C^*$-algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a result on the structure of the relative commutant of a family of generating isometries in a boundary quotient.